What is the foci 5x^2-3x+6 ?

The foci 5x^2-3x+6 is (3/10 , 28/5)

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foci 5x^2-3x+6

foci

5 x^{2} - 3 x + 6

(\frac{3}{10}, \frac{28}{5})

Solution steps

Rewrite

y = 5 x^{2} - 3 x + 6

in the standard form

4 \cdot \frac{1}{20} (y - \frac{111}{20}) = (x - \frac{3}{10})^{2}

(h, k) = (\frac{3}{10}, \frac{111}{20}), p = \frac{1}{20}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(\frac{3}{10}, \frac{111}{20})

along the y-axis

(\frac{3}{10}, \frac{111}{20} + p)

= (\frac{3}{10}, \frac{111}{20} + \frac{1}{20})

Refine

(\frac{3}{10}, \frac{28}{5})

(x + 1)^{2} = - 12 (y - 2)

2 (y - 4) = - \frac{1}{4} (x - 3)^{2}

y \geq x^{2}

x^{2} + 4 x - 1

(x + 5)^{2} = 4 (y - 1)